Problem: Express this quotient in scientific notation: ${\frac{1.680\times 10^{2}} {8.0\times 10^{4}}}$
Answer: Start by collecting like terms together. $= {\frac{1.680} {8.0}} \times{\frac{10^{2}} {10^{4}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.21 \times 10^{2\,-\,4}$ $= 0.21 \times 10^{-2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.21$ is the same as $2.10 \div 10$ , or $2.10 \times 10^{-1}$ $ = {2.10 \times 10^{-1}} \times 10^{-2} $ $= 2.10\times 10^{-3}$